Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON):

Solution:
import pdb
import sys
import math

file = sys.stdin
#file = open("test", "r")

def is_valide(i):
    i *= 2
    root = int(math.sqrt(i))
    if root*(root + 1) == i or (root - 1)*root == i or (root + 1)*(root + 2) == i:
        return True
    else:
        return False

num = int(file.readline().rstrip())
root = int(math.sqrt(num*2) + 1)
for i in range(1, root + 1):
    a = i*(i + 1)/2
    if a >= num:
        continue
    b = num - a
    if is_valide(b):
        print "YES"
        break
else:
    print "NO"